Journal Volume: 153; Conference: Proposed for presentation at the 13th International Conference on Radiation Shielding & 19th Topical Meeting of the Radiation Protection and Shielding Division held October 3-6, 2016 in Paris, Ile-de-France, France.

Subsurface flow processes are inherently three-dimensional and heterogeneous over many scales. Taking this into account, for instance assuming random heterogeneity in 3-D space, puts heavy constraints on numerical models. An efficient numerical code has been developed for solving the porous media flow equations, appropriately generalized to account for 3-D, random-like heterogeneity. The code is based on implicit finite differences (or finite volumes), and uses specialized versions of pre-conditioned iterative solvers that take advantage of sparseness. With Diagonally Scaled Conjugate Gradients, in particular, large systems on the order of several million equations, with randomly variable coefficients, have been solved efficiently onmore » Cray-2 and Cray-Y/MP8 machines, in serial mode as well as parallel mode (autotasking). The present work addresses, first, the numerical aspects and computational issues associated with detailed 3-D flow simulations, and secondly, presents a specific application related to the conductivity homogenization problem (identifying a macroscale conduction law, and an equivalent or effective conductivity). Analytical expressions of effective conductivities are compared with empirical values obtained from several large scale simulations conducted for single realizations of random porous media.« less

Particle transport in rod geometry random media is considered. The cross section is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. An exact closure is constructed for semi-infinite media that yields exact equations for the ensemble averaged angular flux components (or scalar flux {phi} and current J). The same closure scheme yields a Fokker-Planck equation for the joint probability distribution function of {phi} and J, from which ensemble averaged equations for higher order quantities are derived. For a purely scattering semi-infinite medium, the Fokker-Planck equation is solved to get themore » interesting result that the flux and current are non-random quantities. It is argued that this observation is independent of the stochastic model for cross section fluctuations in the problem considered here.« less